Also, a local wild card, Borna Coric, last year's Junior U.S. Open champion, beat qualifier Horacio Zeballos of Argentina 7-6 (4), 6-3 to join Marin Cilic in the quarterfinals, the first time since 2002 two Croats have gone so far in Umag.
In another upset, fourth-seeded Joao Sousa of Portugal, who lost to Cuevas in the Bastad final two weeks ago, fell to Teymuraz Gabashvili of Russia 3-6, 6-4, 6-2.
Fabio Fognini of Italy stayed true to his top seeding by beating Albert Montanes of Spain 7-6 (2), 6-0. Fognini, the 2013 runner-up lost only three points in the 20-minute second set.
Cuevas, riding the confidence of his maiden title in Sweden, didn't drop serve, played patiently from the baseline, and pushed Seppi into unforced errors.
Seppi failed to convert three break points while trailing 5-3 in the first set, and never recovered. He won the first game of the second set, then lost the next six, winning only four points on Cuevas' serve.
Cuevas will play Gabashvili on Friday, after the Russian came from a set and a break down to beat Sousa, a rising star on the tour.
The 17-year-old Coric earned his first win on tour only on Monday, and needed three chances to finish off Zeballos. Coric will face Fognini in the quarterfinals.